Crack elastic-plastic fracture mechanic

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

Ernst, H. A., Elastic Plastic Fracture Mechanics Methodology for Surface Cracks, Georgia Inst, of Tech., 1994. 

It is well known that the methods of elastic-plastic fracture mechanics provide more realistic models of cracked structures with high toughness compared with the methods of the linear elastic fracture mechanics. Ductile materials are used in structural elements not only in piping systems of power plants but in chemical industry, in aircraft propulsion systems and elsewhere [1-8], Evidently, cracked elements in chemical or power plants pose a serious threat to operation of these stmctures. Therefore, it is extremely important that the crack will not spread unstably through the pipe thickness. 

When yielding causes large departures from linearity in the force-displacement curve, such that valid Kiq data cannot be obtained, it is still possible to make geometry-independent measurements of the fracture resistance of the material, using the methods of elastic-plastic fracture mechanics. These usually require additional information to determine whether non-linearity is due to crack tip plasticity alone, or to a combination of plasticity and crack growth. Several different approaches have been developed, of which we will discuss onfy two the crack tip opening displacement (CTOD) and /-integral methods. 

The model Is based on elastic-plastic fracture mechanics principles, and Incorporates effects associated with thermal expansion mismatch and modulus mismatch of various constituents, as well as non-linear material behavior as a function of load and temperature. Key properties of the constituents, such as those of the interlayer, reaction zone, and base material are provided as a data base these data were measured in this program by using bulk samples, The model then uses the processing history, specimen geometry and loading conditions to evaluate the performance of the joint, The results of finite element analysis of cracked specimens have been consolidated In arriving at the engineering model, JADM,... 

Fig. 5.10. Failure-assessment diagram (after [21]) in standardised form for Y = const. The arrows show how the state of the loaded component changes when the corresponding parameter is raised. Thus, increasing the limiting stress criimit or the initial crack length a increases the tendency for failure by crack propagation, whereas increasing the fracture toughness Kic decreases it. Within the region marked with EPFM, elastic-plastic fracture mechanics has to be used because the plastic zone near the crack tip is not small. This theory is the topic of section 5.3...

In the previous sections, it was frequently stressed that linear-elastic fracture mechanics can only be used if the plastic zone near the crack tip is sufficiently small. If this is not the case, we enter the domain of elastic-plastic fracture mechanics (epfm) which can deal with a large plastic zone. The method, however, cannot be used for arbitrarily large plastic zones - plastic behaviour must stiU be restricted to the region around the crack tip and must be mainly determined by the surrounding elastic stress field. 

As in linear-elastic fracture mechanics, specimens in elastic-plastic fracture mechanics are also standardised. An initial crack is produced in the same way by cyclic loading. The values of the J integral for crack propagation, Jc and J, are read off the Jr crack-growth resistance curve, so there is no need to perform additional experiments. 

Rice was the first to recognize the potential use of J-integral in elastic-plastic fracture mechanics, after Eshelby was apparently the first to derive the integral [1 3]. The J-integral of a critical crack, Jc, is actually equivalent to Rc defined in Eq. (2) combined with the schematic procedure in Fig. 2. For the case of a plate containing a deep notch and subjected to pure bending, Rice found that [1 3]... 

Substantial work on the appHcation of fracture mechanics techniques to plastics has occurred siace the 1970s (215—222). This is based on earlier work on inorganic glasses, which showed that failure stress is proportional to the square root of the energy required to create the new surfaces as a crack grows and iaversely with the square root of the crack size (223). For the use of linear elastic fracture mechanics ia plastics, certaia assumptioas must be met (224) (/) the material is linearly elastic (2) the flaws within the material are sharp and (J) plane strain conditions apply ia the crack froat regioa. 

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